Final answer:
The growth constant, k, is approximately 0.08093. The estimated population after 25 years is approximately 113,485. The estimated doubling time for the town's population is approximately 8.54 years.
Step-by-step explanation:
To find the growth constant, k, we can use the formula:
k = ln(P2/P1)/t
where P1 is the initial population, P2 is the final population, and t is the time in years. Given that P1 = 15000, P2 = 20000, and t = 5, we can substitute these values into the formula:
k = ln(20000/15000)/5 = ln(4/3)/5
Approximately, k = 0.08093.
The exponential model of the population of Tanjung Kota is therefore given by:
P(t) = P(0)ekt
To estimate the population after 25 years, we substitute t = 25 into the exponential model:
P(25) = 15000 * e0.08093*25 ≈ 15000 * e2.02325 ≈ 15000 * 7.5655622 ≈ 113484.93
Hence, the estimated population after 25 years is approximately 113,485.
To estimate the doubling time for the town's population, we can use the formula:
td = ln(2)/k
By substituting the value of k, we get:
td = ln(2)/0.08093 ≈ 8.54
Hence, the estimated doubling time for the town's population is approximately 8.54 years.
Learn more about Exponential Growth